Neuro-evolutionary evidence for a universal fractal primate brain shape

The primate cerebral cortex can take on a bewildering diversity of shapes and sizes within and across species, whilst maintaining archetypal qualities that make it instantly recognisable as a "brain". Here we present a new way of expressing the shape of a cortex explicitly as the hierarchical composition of structures across spatial scales. In computational simulations, as one successively removes sulci and gyri smaller than a specified scale, the cortices of 11 primate species are gradually coarse-grained into less folded brains until lyssencephaly (no folding). We show that this process, in all cases, occurs along a common scale-free morphometric trajectory overlapping with other mammalian species, indicating that these cortices are not only approximately fractal in shape, but also, strikingly, are approximations of the same archetypal fractal shape. These results imply the existence of a single universal gyrification mechanism that operates in a scale-free manner on cortical folds of all sizes, and that there are surprisingly few effective degrees of freedom through which cortical shapes can be selected for by evolution. Finally, we demonstrate that this new understanding can be of practical use: biological processes can now be interrogated in a highly scale-dependent way for increased sensitivity and precision. To our knowledge, this is the most parsimonious universal description of the brain's shape that is at the same time mechanistically insightful, practically useful, and in full agreement with empirical data across species and individuals.